# Full text of "Analytical Mechanics"

## See other formats

```ENERGY                                       1!
5.   How many cubic miles of ice could be melted by the heat comput in the preceding problem?   The latent heat of ice is 80 calories per gra:
6.   The winder of a spinning top is a helical spring, which is set in cylindrical piece 1 inch in diameter.   When the winder is hooked to t top and twisted through TT radians a force of 1 pound has to be applied the cylinder tangentially in order to keep it from untwisting itself.   Af1 the spring is given a twist of^J turns the top is released.   Find the kine-energy the top would acquire if there were no frictional forces.
7.   In the preceding problem find the angular velocity of the top suppc ing it to consist of a circular plate of 2 inch radius, and of J pound weig]
8.   If the top of the preceding problem turns for 2 minutes before stc ping, find the mean torque due to friction and resistance; also find t total number of revolutions made.
9.   A top is given a motion of rotation by pulling at a string wou: around it.   Derive an expression for the energy communicated, (a) wh
• the force applied to the string is constant; (b) when it varies directly wi the length of the string which is unwound.
POWER.
157. Power. — Power is the rate at which work is don When put into the language of calculus this definition b comes
P = ^-                               (VI
at
Power is a scalar quantity and has the dimensions [ML2T~ The C.G.S. unit of power is the erg per second. This ui is too small for engineering purposes; therefore two larg units are adopted, which are called the watt and the kilowa The following relations define these units :
-,      <L<L    1 joule 1 watt = —~ -1 sec.
sec. 1 kilowatt = 103 watts
= 1010-
sec.```